Internal consistency of fault-tolerant quantum error correction in light of rigorous derivations of the quantum Markovian limit

Robert Alicki, Daniel A. Lidar, and Paolo Zanardi
Phys. Rev. A 73, 052311 – Published 15 May 2006

Abstract

We critically examine the internal consistency of a set of minimal assumptions entering the theory of fault-tolerant quantum error correction for Markovian noise. These assumptions are fast gates, a constant supply of fresh and cold ancillas, and a Markovian bath. We point out that these assumptions may not be mutually consistent in light of rigorous formulations of the Markovian approximation. Namely, Markovian dynamics requires either the singular coupling limit (high temperature), or the weak coupling limit (weak system-bath interaction). The former is incompatible with the assumption of a constant and fresh supply of cold ancillas, while the latter is inconsistent with fast gates. We discuss ways to resolve these inconsistencies. As part of our discussion we derive, in the weak coupling limit, a new master equation for a system subject to periodic driving.

  • Received 10 February 2006

DOI:https://doi.org/10.1103/PhysRevA.73.052311

©2006 American Physical Society

Authors & Affiliations

Robert Alicki1, Daniel A. Lidar2, and Paolo Zanardi3

  • 1Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Poland
  • 2Departments of Chemistry, Electrical Engineering-Systems, and Physics, University of Southern California, Los Angeles, California 90089, USA
  • 3Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy

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Issue

Vol. 73, Iss. 5 — May 2006

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